PDE lecture_04.pdf DDE hw_04.pdf X DDE lecture_03.pdf + V X -> . . . Q A file:///C:/Users/82109/Desktop/hw_04.pdf X 1 (50 pts). Use scan("It. txt") to read in the data from the file It. txt, which is a vector of length 500. Consider a local trend model for the data yt = St + et, et ~ N(0, 0.25); St+1 = St +nt, 71t ~ N(0, 0.01), So ~ N(0.2, 2.25). Use your own program for part (a), (b), and (c). (a) Write your own program to implement the Kalman filter. Calculate the exact log likelihood of the data. [Hint. Use $1/0 = 0.2, and 21jo = 2.26 as the initial values.] (b) Plot the predicted state variables $t)t-1 for 1